Hello
Most people keep quail and chickens separate because of the risk of chickens giving the quail diseases. The chickens aren't symptomatic but possible carriers and can kill all of your quail very quickly if they get infected.
For this reason, good bio security is practiced to reduce the chances of possible infection. This involves stuff like keeping the different birds in different locations on the property, washing hands between interacting/feeding/watering between the two as well as germs on your shoes that you could track to the quail.
Disease risk aside, have you witnessed bullying/pecking order between chickens? It can get pretty vicious with blood sometimes so you can imagine a way smaller derpy quail getting one peck because it got too close to the food the chicken wanted and getting seriously injured or even killed.
They scalp VERY easily just from other quail fights and aren't faster or smarter than the chickens - quail bites are like a dog lick compared to a chickens bite which gives adult people bruises and tears skin.
The quail also don't speak chicken so certain postures or sounds wouldn't be heeded so they can easily wind up doing what the chickens think needs a pecking/dominated.
I have seen chicken jump on top of other chickens and rip a clump of feathers off while kicking off of the bird, making it extra savage, I have also seen them hunt a big frog similar to quail size and shake it ferociously and they also hunted down and ate a mouse in the yard. One vicious shake by a chicken and the small animal is dead so quail wouldn't be safe in my opinion in the same run as chickens
We literally call our four chickens little raptors and they strut around the yard like a gang, killing anything small enough to eat xD
